We look at the division of 41100567 by 681 
We want to divide 41100567 by 681.

Going ahead to step 1:
If we divide 4 by 681, we get 0 and a remainder of 4.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtract 0 from 4 to get 4.
Append the next digit (1) from the dividend to 4 and continue with: 41 / 681

Step 2:
681 goes into 41 0 times with a remainder of 41.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtracting 0 from 41 leaves us with 41.
Bring next digit (1) of the dividend behind the 41 and repeat the process: 411 / 681

Moving on to step 3:
411 divided by 681 is 0 with a remainder of 411.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we take 0 away from 411, we end up with 411.
Append the next digit (0) from the dividend to 411 and continue with: 4110 / 681

Moving on to step 4:
681 can be fit into 4110 6 times, resulting in a remainder of 24.
Record the quotient 6 as the next digit in the result. 
Result so far: 6.0
The remainder is 24 after subtracting 4086 from 4110.
Fetch the next digit (0) from the dividend, attach it to 24 and continue: 240 / 681

Advancing to step 5:
681 goes into 240 0 times with a remainder of 240.
Record the quotient 0 as the next digit in the result. 
Result so far: 60.0
Deduct 0 from 240 and we're left with 240.
Grab the next digit (5) from the dividend, add it to 240, then carry on: 2405 / 681

Going ahead to step 6:
If we divide 2405 by 681, we get 3 and a remainder of 362.
Record the quotient 3 as the next digit in the result. 
Result so far: 603.0
Subtracting 2043 from 2405 leaves us with 362.
Append the next digit (6) from the dividend to 362 and continue with: 3626 / 681

Moving on to step 7:
681 can be fit into 3626 5 times, resulting in a remainder of 221.
Record the quotient 5 as the next digit in the result. 
Result so far: 6035.0
Subtracting 3405 from 3626 leaves us with 221.
Grab the next digit (7) from the dividend, add it to 221, then carry on: 2217 / 681

On to step 8:
When dividing 2217 by 681, we get 3 with a remainder of 174.
Put 3 as the next digit of the answer. 
Result so far: 60353.0
If we take 2043 away from 2217, we end up with 174.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1740, and continue the process.

Let's proceed to step 9:
681 goes into 1740 2 times with a remainder of 378.
Use 2 as the next digit of our solution. 
Result so far: 60353.2
Subtracting 1362 from 1740 leaves us with 378.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3780, and continue the process.

Advancing to step 10:
When dividing 3780 by 681, we get 5 with a remainder of 375.
The number 5 becomes the next digit in our result. 
Result so far: 60353.25
If we take 3405 away from 3780, we end up with 375.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3750, and continue the process.

Advancing to step 11:
The number 681 fits into 3750 5 times, leaving a remainder of 345.
The number 5 becomes the next digit in our result. 
Result so far: 60353.255
If we take 3405 away from 3750, we end up with 345.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3450, and continue the process.

The final result is 60353.255 with a remainder of 0.0345.